My roommate just had this problem with Microsoft Word 2003, and I found the fix using the Google search engine. Here’s what you do:
Tools -> Options -> Edit
Check “Typing Replaces Selection”
That’s all my roommate had to do. For the sake of completeness, the fix also says:
Tools -> Options -> General
Uncheck both options that have WordPerfect in them
Hope this helps someone.

Thank you so much for this tip. It was quite aggravating to deal with this problem. You Rock!
thanks for the easy fix!
Thanks, this has been hurting my brain for a few days, my fingers are just too used to the backspace key!
Danke!
“Hope this helps someone” - you have no idea. Thank you.